 #1
Lindsayyyy
 219
 0
Homework Statement
Is the following equation a total derivative?
[tex] dz = 2ln(y)dx+{\frac x y}dy[/tex]
Homework Equations

The Attempt at a Solution
I would say no. I tried it with the symmetry of the second derivatives.
[tex] 2ln(y) [/tex] is [tex] {\frac {\partial z} {\partial x}}[/tex]
when I derivate it now and say y is my variable I get:
[tex] {\frac {\partial z} {\partial y}}=\frac 2 y[/tex]
same for the other expression
[tex] {\frac {\partial z} {\partial y}}=\frac x y[/tex]
[tex] {\frac {\partial z} {\partial x}}=\frac 1 y[/tex]
so they are different => no totale derivative. Am I right or where did I do mistakes?
Thanks for the help